bib.tex

Concrete_Mathematics_2nd_Ed_TeX_Source_Code

Submitted for publication in 1778.
Reprinted in his {\sl Opera Omnia}, series~1, volume~16(2), 41--55.

\bib|faulhaber|%
Johann "Faulhaber"n, {\sl Academia Algebr\ae}, Darinnen die miraculosische
Inventiones zu den h\"ochsten Cossen weiters {\it continuirt\/} und
{\it profitiert\/} werden, \dots~bi\ss\ auff die regulierte
{\it Zensicubiccubic\/} Co\ss\ durch offnen Truck {\it publiciert\/} worden. \
Augsburg, 1631.

\bib|feller|%
William "Feller", {\sl An Introduction to Probability Theory and
Its Applications}, volume~1. \
Wiley, 1950; second edition, 1957; third edition, 1968.

\bib|fermat|%
Pierre de "Fermat", letter to Marin "Mersenne" (25~December 1640), in
{\sl \OE uvres de Fermat}, volume~2, 212--217.

\bib|fibonacci|%
Leonardo "Fibonacci" ["Pisano"], {\sl Liber Abaci}. \
First edition, 1202 (now lost); second edition, 1228. Reprinted in
{\sl Scritti di Leonardo Pisano}, edited by Baldassarre "Boncompagni",
1857, volume~1.

\bib|de-finetti|%
Bruno de "Finetti", {\sl Teoria delle Probabilit\`a.} \ Turin, 1970.
English translation, {\sl Theory of Probability}, Wiley, 1974--1975.

\bib|fisher|%
Michael E. "Fisher", ``Statistical mechanics of dimers on a plane
lattice,'' {\sl Physical Review\/ \bf124} (1961), 1664--1672.

\bib|ra-fisher|%
R.\,A. "Fisher", ``Moments and product moments of sampling distributions,''
{\sl Proceedings of the London Mathematical Society}, series 2,
{\bf30} (1929), 199--238.

\bib|forcadel|%
Pierre "Forcadel", {\sl L'arithmeticque}. \ Paris, 1557.

\bib|fourier|%
J. "Fourier", ``Refroidissement s\'eculaire du globe terrestre,''
{\sl Bulletin des Sciences par la Soci\'et\'e philomathique de Paris}, series 3,
{\bf7} (1820), 58--70. Reprinted in {\sl \OE uvres de Fourier}, volume~2,
271--288.

\bib|fraenkel-cover|%
Aviezri S. "Fraenkel", ``Complementing and exactly covering sequences,''
{\sl Journal of Combinatorial Theory}, series~A, {\bf14} (1973), 8--20.

\bib|fraenkel-wyt|%
Aviezri S. "Fraenkel", ``How to beat your "Wythoff" games' opponent on three
fronts,'' {\sl American Mathematical Monthly\/ \bf89} (1982), 353--361.

\bib|amm-hanoi|%
J.\,S. "Frame", B.\,M. "Stewart", and Otto "Dunkel",
``Partial solution to problem 3918,''
{\sl American Mathematical Monthly\/ \bf48} (1941), 216--219.

\bib|pacioli|%
Piero della "Francesca", {\sl Libellus de
quinque corporibus regularibus.} \ Vatican Library, manuscript Urbinas~632.
Translated into Italian by Luca "Pacioli", as part~3 of
Pacioli's {\sl Diuine Proportione}, Venice, 1509.

\bib|franel|%
J. "Franel", Solutions to questions 42 and 170, in
{\sl L'Interm\'ediare des Math\'ematiciens\/ \bf1} (1894),
45--47; {\bf2} (1895), 33--35.

\bib|samplesort|%
W.\,D. "Frazer" and A.\,C. "McKellar", ``Samplesort: A sampling approach
to minimal storage tree sorting,''
{\sl Journal of the ACM\/ \bf27} (1970), 496--507.

\bib|fredman-thesis|%
Michael Lawrence "Fredman", {\sl Growth Properties of a Class of
Recursively Defined Functions}. \
Ph.D. thesis, Stanford University, Computer Science Department, 1972.

\bib|fuss|%
Nikolao "Fuss", ``Solutio qu\ae stionis, quot modis polygonum $n$
laterum in polygona $m\mskip1mu$ laterum, per diagonales resolvi qu{\ae}at,''
{\sl Nova acta academi{\ae} scientiarum imperialis Petropolitan{\ae}\/ \bf9}
(1791), 243--251.

\bib|gardner-phi|%
Martin "Gardner", ``About phi, an irrational number that has some
remarkable geometrical expressions,''
{\sl Scientific American\/ \bf201},\,2 (August 1959), 128--134. Reprinted
with additions
in his book {\sl The 2nd Scientific American Book of Mathematical Puzzles
\& Diversions}, 1961, 89--103.

\bib|gardner-coins|%
Martin "Gardner", ``On the paradoxical situations that arise from nontransitive
relations,'' {\sl Scientific American\/ \bf231},\,4
(October 1974), 120--124. Reprinted with additions
in his book {\sl Time Travel
and Other Mathematical Bewilderments}, 1988, 55--69.

\bib|gardner-rope|%
Martin "Gardner", ``From rubber ropes to rolling cubes, a miscellany of
refreshing problems,'' {\sl Scientific American\/ \bf232},\,3
(March 1975), 112--114; {\bf232},\,4 (April 1975), 130, 133.
 Reprinted with additions in his book {\sl Time Travel
and Other Mathematical Bewilderments}, 1988, 111--124.

\bib|gardner-dice|%
Martin "Gardner", ``On checker jumping, the amazon game, weird dice, card
tricks and other playful pastimes,'' {\sl Scientific American\/ \bf238},\,2
(February 1978), 19, 22, 24, 25, 30, 32.
Reprinted with additions in his book {\sl Penrose Tiles to Trapdoor Ciphers},
1989, 265--280.

\bib|garfunkel|%
J. "Garfunkel", ``Problem E\,1816: An inequality related to Stirling's
formula,'' {\sl American Mathematical Monthly\/ \bf74} (1967), 202.

\bib|gasper-rahman|%
George "Gasper" and Mizan "Rahman", {\sl Basic Hypergeometric Series}. \
Cambridge University Press, 1990.

\bib|gauss-disq|%
C.\,F. "Gauss", {\sl Disquisitiones Arithmetic\ae}. \
Leipzig, 1801. Reprinted in his {\sl Werke}, volume~1.

\bib|gauss-hyp|%
Carolo Friderico "Gauss", ``Disquisitiones generales circa seriem
infinitam
\begindisplay \openup2pt
&1+{\alpha\beta\over1\,.\,\gamma}\,x
 +{\alpha(\alpha+1)\beta(\beta+1)\over1\ .\ 2\ .\ \gamma(\gamma+1)}\,xx\cr
&\qquad +{\alpha(\alpha+1)(\alpha+2)\beta(\beta+1)(\beta+2)\over
    1\ .\ 2\ .\ 3\ .\ \gamma(\gamma+1)(\gamma+2)}x^3+\rm etc.
\enddisplay
Pars prior,'' {\sl Commentationes societatis regi\ae\ scientiarum Gottingensis
recentiores\/ \bf2} (1813). (Thesis delivered to the Royal Society in
G\"ottingen, 20~January 1812.)
 Reprinted in his {\sl Werke}, volume~3, 123--163,
together with an unpublished sequel on pages 207--229.

\bib|gauss-penta|%
C.\,F. "Gauss", ``Pentagramma mirificum,'' written prior to 1836.
Published posthumously in his {\sl Werke}, volume~3, 480--490.

\bib|genocchi|%
A. "Genocchi", ``Intorno all' expressioni generali di numeri Bernoulliani,''
{\sl Annali di Scienze Matematiche e Fisiche\/ \bf3} (1852), 395--405.

\bib|gessel-apery|%
Ira "Gessel", ``Some congruences for Ap\'ery numbers,''
{\sl Journal of Number Theory\/ \bf14} (1982), 362--368.

\bib|gessel-stanley|%
Ira "Gessel" and Richard P. "Stanley", ``Stirling polynomials,''
{\sl Journal of Combinatorial Theory}, series~A, {\bf24} (1978), 24--33.

\bib|ginsburg|%
Jekuthiel "Ginsburg", ``Note on Stirling's numbers,''
{\sl American Mathematical Monthly\/ \bf35} (1928), 77--80.

\bib|glaisher|%
J.\,W.\,L. "Glaisher", ``On the product
$1^1.2^2.3^3\ldots n^n$, {\sl Messenger of Mathematics\/ \bf7} (1877),
43--47.

\bib|golomb-self|%
Solomon W. "Golomb", ``Problem 5407: A nondecreasing indicator function,''
{\sl American Mathematical Monthly\/ \bf74} (1967), 740--743.

\bib|sales-tax|%
Solomon W. "Golomb", ``The `Sales Tax' theorem,'' {\sl Mathematics
Magazine\/ \bf49} (1976), 187--189.

\bib|golomb-sum|%
Solomon W. "Golomb", ``Problem E\,2529: An application of $\psi(x)$,''
{\sl American Mathematical Monthly\/ \bf83} (1976), 487--488.

\bib|good|%
I.\,J. "Good", ``Short proof of a conjecture by "Dyson",'' {\sl Journal
of Mathematical Physics\/ \bf11} (1970), 1884.

\bib|gosper|%
R. William "Gosper", Jr., ``Decision procedure for indefinite hypergeometric
summation,'' {\sl Proceedings of the National Academy of Sciences of the
United States of America\/
\bf75} (1978), 40--42.

\bib|young-ron|%
R.\,L. "Graham", ``On a theorem of "Uspensky",''
{\sl American Mathematical Monthly\/ \bf70} (1963), 407--409.

\bib|graham-fib-composites|%
R.\,L. "Graham", ``A Fibonacci-like sequence of composite numbers,''
{\sl Mathematics Magazine\/ \bf37} (1964), 322--324.

\bib|graham-amm|%
R.\,L. "Graham", ``Problem 5749,''
{\sl American Mathematical Monthly\/ \bf77} (1970), 775.

\bib|graham-cover|%
Ronald L. "Graham", ``Covering the positive integers by disjoint sets of the
form $\{\,[n\alpha+\beta]:n=1,2,\ldots\,\,\}$,''
{\sl Journal of Combinatorial Theory}, series A, {\bf15} (1973), 354--358.

\bib|graham-squareprod|%
R.\,L. "Graham", ``Problem 1242: Bijection between integers and composites,''
{\sl Mathematics Magazine\/ \bf60} (1987), 180.

\bib|graham-knuth|%
R.\,L. "Graham" and D.\,E. "Knuth", ``Problem E\,2982: A double
infinite sum for $\vert x\vert$,''
{\sl American Mathematical Monthly\/ \bf96} (1989), 525--526.

\bib|conc-math|%
Ronald L. "Graham", Donald E. "Knuth", and Oren "Patashnik", {\sl Concrete
Mathematics: A Foundation for Computer Science}. \
"!self-referential"
Addison-Wesley, 1989; second edition, 1994.

\bib|graham-pollak|%
R.\,L. "Graham" and H.\,O. "Pollak", ``Note on a nonlinear recurrence related
to $\sqrt2$,'' {\sl Mathematics Magazine\/ \bf43} (1970), 143--145.

\bib|grandi|%
Guido "Grandi", letter to "Leibniz" (July 1713), in
{\sl Leibnizens mathematische Schriften}, volume~4, 215--217.

\bib|greene-knuth|%
Daniel H. "Greene" and Donald E. "Knuth", {\sl Mathematics for the
Analysis of Algorithms}. \
Birkh\"auser, Boston, 1981; third edition, 1990.

\bib|olympiads1|%
Samuel L. "Greitzer", {\sl International Mathematical Olympiads, 1959--1977}. \
Mathematical Association of America, 1978.

\bib|gross|%
Oliver A. "Gross", ``Preferential arrangements,''
{\sl American Mathematical Monthly\/ \bf69} (1962), 4--8.

\bib|gruenbaum|%
Branko "Gr\"unbaum", ``Venn diagrams and independent families of sets,''
{\sl Mathematics Magazine\/ \bf48} (1975), 12--23.

\bib|guibas-odlyzko|%
L.\,J. "Guibas" and A.\,M. "Odlyzko", ``String overlaps, pattern matching,
and nontransitive games,'' {\sl Journal of Combinatorial Theory},
series~A, {\bf30} (1981), 183--208.

\bib|guy|%
Richard K. "Guy", {\sl Unsolved Problems in Number Theory}. \
Springer-Verlag, 1981.

\bib|haaland-knuth|%
Inger "H{\aa}land" and Donald E. "Knuth", ``Polynomials involving the
floor function,'' submitted for publication, 1993.

\bib|hall-groups|%
Marshall "Hall", Jr., {\sl The Theory of Groups}. \
Macmillan, 1959.

\bib|halmos-write|%
P.\,R. "Halmos", ``How to write mathematics,''
{\sl L'Enseignement math\'e\-ma\-tique\/ \bf16} (1970), 123--152.
Reprinted in {\sl How to Write Mathematics}, American Mathematical
Society, 1973, 19--48.

\bib|halmos-auto|%
Paul R. "Halmos", {\sl I Want to Be a Mathematician: An Automathography}. \
Springer-Verlag, 1985. Reprinted by Mathematical Association of America, 1988.

\bib|halphen|%
G.\,H. "Halphen", ``Sur des suites de fractions analogues \`a la suite
 de "Farey",''
{\sl Bulletin de la Soci\'et\'e math\'ematique de France\/ \bf5} (1876),
170--175. Reprinted in his {\sl \OE uvres}, volume~2, 102--107.

\bib|hamburger|%
Hans "Hamburger", ``\"Uber eine Erweiterung des "Stieltjes"schen
 Momentenproblems,''
{\sl Mathematische Annalen\/ \bf81} (1920), 235--319; {\bf82} (1921),
120--164, 168--187.

\bib|hammersley|%
J.\,M. "Hammersley", ``On the enfeeblement of mathematical skills
by `Modern Mathematics'
and by similar soft intellectual trash in schools and universities,''
{\sl Bulletin of the Institute of Mathematics and its Applications\/
\bf4},\,4 (October 1968), 66--85.

\bib|hammersley-undergrad|%
J.\,M. "Hammersley", ``An undergraduate exercise in manipulation,''
{\sl The Mathematical Scientist\/ \bf14} (1989), 1--23.

\bib|hansen|%
Eldon R. "Hansen", {\sl A Table of Series and Products}. \
Prentice-Hall, 1975.

\bib|hardy-tract|%
G.\,H. "Hardy", {\sl Orders of Infinity: The `Infinit\"arcalc\"ul' of
Paul du "Bois-Reymond"}. Cambridge University Press, 1910;
second edition, 1924.

\bib|hardy-golf|%
G.\,H. "Hardy", ``A mathematical theorem about golf,''
{\sl The Mathematical Gazette\/ \bf29} (1944), 226--227. Reprinted
in his {\sl Collected Papers}, volume~7, 488.

\bib|hardy-wright|%
G.\,H. "Hardy" and E.\,M. "Wright", {\sl An Introduction to the Theory of
Numbers}. \ Clarendon Press, Oxford, 1938; fifth edition, 1979.

\bib|henrici|%
Peter "Henrici", {\sl Applied and Computational Complex Analysis}.
Wiley, volume~1, 1974; volume~2, 1977; volume~3, 1986.

\bib|henrici-bieberbach|%
Peter "Henrici", ``"De Branges"' proof of the "Bieberbach" conjecture:
A view from computational analysis,'' {\sl Sitzungsberichte der
Berliner Mathematischen Gesellschaft\/} (1987), 105--121.

\bib|hermite-staudt|%
Charles "Hermite", letter to C.\,W. "Borchardt" (8 September 1875), in
{\sl Journal f\"ur die reine und angewandte Mathematik\/ \bf81}
 (1876), 93--95. Reprinted in his
{\sl \OE uvres}, volume~3, 211--214.

\bib|hermite-cours|%
Charles "Hermite", {\sl Cours de M. Hermite}. \
Facult\'e des Sciences de Paris, 1882. Third edition, 1887; fourth edition, 1891.
% capital S is correct in spite of the library card

\bib|hermite|%
Charles "Hermite", letter to S. "Pincherle" (10~May 1900), in
{\sl Annali di Matematica pura ed applicata}, series 3, {\bf5}
(1901), 57--60. Reprinted in his
{\sl \OE uvres}, volume~4, 529--531.

\bib|herstein-kaplansky|%
I.\,N. "Herstein" and I. "Kaplansky", {\sl Matters Mathematical}. \
Harper \& Row, 1974.